基于MCMC模拟的MGPD模型及其在地质灾害风险度量中的应用

基于马尔科夫链蒙特卡洛(简记为MCMC)模拟的参数贝叶斯估计,对改进的广义帕累托分布(简记为MGPD)模型进行了优化,并利用该模型得到了地质灾害损失的在险损失值(简记为VaR)和条件损失值(简记为CVaR).以湖南娄底市地质灾害损失数据进行实证分析及模型适应性检验,结果表明:优化后的模型不仅具有很好的极值数据描述能力,而且具有较强的适用性.     

极值理论及其在巨灾再保险定价中的应用

巨灾损失中往往存在极端值,一般统计分布对其拟合效果欠佳,本文运用极值理论对极端值建模,基于分层定价的思想,在不同的起赔点下对再保险超额损失部分的定价进行了探讨,并以洪水损失数据为例进行了实证研究,拟合了POT模型,得到了洪水再保险纯保费。     

尖峰厚尾保险损失数据的统计建模

保险损失数据的一个重要特点是尖峰厚尾性,即既有大量的小额损失,又有少量的高额损失,使得通常的损失分布模型很难拟合此类数据,从而出现了对各种损失分布模型进行改进的尝试.改进后的模型一方面要有较高的峰度,另一方面又要有较厚的尾部.最近几年文献中出现的改进模型主要是组合模型,即把一个具有非零众数的模型(如对数正态分布或威布尔分布)与一个厚尾分布模型(如帕累托分布或广义帕累托分布)进行组合.讨论了这些组合模型的性质和特点,并与偏t正态分布和偏t分布进行了比较分析,最后应用MCMC方法估计模型参数,并通过一个实际损失数据的拟合分析,表明偏t分布对尖峰厚尾损失数据的拟合要优于目前已经提出的各种组合模型.     

基于伽玛与对数正态分布假设下的广义线性模型的比较和应用

本文在假设每次损失金额的变异系数相同,且它们服从伽玛分布或对数正态分布的条件下,讨论了加法模型和乘法模型的参数估计和拟合优度检验,并应用一组实际损失数据对上述模型进行了实证比较。结果表明,对于一组特定的损失数据,对数正态分布假设下的广义线性模型可能优于伽玛分布假设下的广义线性模型。     

多损失WCVaR模型的等价性定理

研究了多概率分布簇下的多损失下的WCVaR(Multi Worst Conditional Value-at-Risk)模型等价性定理, 根据概率分布簇的VaR测度值, 定义了多损失下的WCVaR风险测度值和对应的多目标优化模型(MWCVaR), 证明了多目标优化模型(MWCVaR)等价另一个多目标优化模型求解. 对于有限分布簇情形, 在一定条件下, 证明了用有限个分布簇就可以近似计算多损失(MWCVaR)优化模型.     

医疗保险定点医院损失分布估计

本文应用了风险模型的损失分布及其估计方法,在分析社会医疗保险医疗赔付模式下,根据定点医院相关数据对风险模型的损失分布进行了实证分析和估计。并采用蒙特卡罗方法进行了数据仿真,表明估计结果的有效性     

汽车交通事故损失分布的尾部估计

由于巨额损失对保险公司的影响非常大,费率厘定过程中对极值分布的研究非常重视。本文从极值理论的角度出发,以上海市虹口区2003年的汽车交通事故损失数据为样本,探讨了损失分布的尾部估计方法,并利用该地区2006年的汽车交通事故损失对结论进行了验证。研究结果发现,广义帕雷托分布确实对损失额的尾部提供了较好的拟合,但这依赖于门槛值的恰当选择。传统的门槛值选择方法主观性较强,而通过重复多次的交叉验证技巧,我们可以估计广义帕雷托分布的最合适门槛值位置。     

基于POT模型的巨灾风险度量与保险模式研究——以地震风险为例

巨灾风险发生的频率低且损失大,具有显著的厚尾性特征,因此不易度量其风险。本文以地震风险为例,采用1961-2011年以来中国发生的4.5级以上地震造成的损失值作为样本,在进行物价调整之后引入了POT模型和广义Pareto分布对损失数据进行拟合,计算出不同的置信度水平下不同的VaR值,得到不同的保费规模与地震保险的价格,并以此为依据设计我国巨灾保险的风险分散机制。     

基于贝叶斯极值估计的商业银行内部欺诈风险度量研究

内部欺诈风险是我国商业银行面临的一个重大风险来源。本文针对内部欺诈具有的低频率高损失的特点,采用不同分布分段刻画其损失统计分布规律,对于低于和高于门限值的样本点,采用Box-Cox变换和全Paretian分布模型进行分析,然后采用贝叶斯估计对全Paretian分布模型的参数进行估计,接着在此基础上对建立了一个内部欺诈风险度量模型,然后使用所构建的风险度量模型对操作风险在险风险值、经济资本和最大可能损失进行了测算,最后提出了防范操作风险的政策建议。     

基于分位数回归模型的地震巨灾风险评估

地震损失数据存在明显的厚尾特征,使得通常的均值回归模型因为容易受到极端值的影响而无法适用。本文对传统的分位数回归模型和函数系数的分位数回归模型进行了比较研究,分析了它们的优缺点,并基于我国大陆地区1990-2015年的地震灾害损失数据,重点探讨了它们在我国地震巨灾风险管理中的应用,计算了不同震级和置信水平下,我国地震灾害损失的VaR和TVaR等风险度量值。基于前述结果,本文最后还探讨了我国地震巨灾指数保险的设计和费率厘定问题。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.